MAYBE
Time: 0.031565
TRS:
 {           le(0(), y) -> true(),
           le(s x, 0()) -> false(),
           le(s x, s y) -> le(x, y),
               pred s x -> x,
          minus(x, 0()) -> x,
          minus(x, s y) -> pred minus(x, y),
            gcd(0(), y) -> y,
          gcd(s x, 0()) -> s x,
          gcd(s x, s y) -> if_gcd(le(y, x), s x, s y),
   if_gcd(true(), x, y) -> gcd(minus(x, y), y),
  if_gcd(false(), x, y) -> gcd(minus(y, x), x)}
 DP:
  DP:
   {         le#(s x, s y) -> le#(x, y),
            minus#(x, s y) -> pred# minus(x, y),
            minus#(x, s y) -> minus#(x, y),
            gcd#(s x, s y) -> le#(y, x),
            gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y),
     if_gcd#(true(), x, y) -> minus#(x, y),
     if_gcd#(true(), x, y) -> gcd#(minus(x, y), y),
    if_gcd#(false(), x, y) -> minus#(y, x),
    if_gcd#(false(), x, y) -> gcd#(minus(y, x), x)}
  TRS:
  {           le(0(), y) -> true(),
            le(s x, 0()) -> false(),
            le(s x, s y) -> le(x, y),
                pred s x -> x,
           minus(x, 0()) -> x,
           minus(x, s y) -> pred minus(x, y),
             gcd(0(), y) -> y,
           gcd(s x, 0()) -> s x,
           gcd(s x, s y) -> if_gcd(le(y, x), s x, s y),
    if_gcd(true(), x, y) -> gcd(minus(x, y), y),
   if_gcd(false(), x, y) -> gcd(minus(y, x), x)}
  UR:
   {   le(0(), y) -> true(),
     le(s x, 0()) -> false(),
     le(s x, s y) -> le(x, y),
         pred s x -> x,
    minus(x, 0()) -> x,
    minus(x, s y) -> pred minus(x, y),
          a(z, w) -> z,
          a(z, w) -> w}
   EDG:
    {(gcd#(s x, s y) -> le#(y, x), le#(s x, s y) -> le#(x, y))
     (if_gcd#(false(), x, y) -> minus#(y, x), minus#(x, s y) -> minus#(x, y))
     (if_gcd#(false(), x, y) -> minus#(y, x), minus#(x, s y) -> pred# minus(x, y))
     (minus#(x, s y) -> minus#(x, y), minus#(x, s y) -> minus#(x, y))
     (minus#(x, s y) -> minus#(x, y), minus#(x, s y) -> pred# minus(x, y))
     (gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y), if_gcd#(true(), x, y) -> minus#(x, y))
     (gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y), if_gcd#(true(), x, y) -> gcd#(minus(x, y), y))
     (gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y), if_gcd#(false(), x, y) -> minus#(y, x))
     (gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y), if_gcd#(false(), x, y) -> gcd#(minus(y, x), x))
     (if_gcd#(true(), x, y) -> minus#(x, y), minus#(x, s y) -> pred# minus(x, y))
     (if_gcd#(true(), x, y) -> minus#(x, y), minus#(x, s y) -> minus#(x, y))
     (le#(s x, s y) -> le#(x, y), le#(s x, s y) -> le#(x, y))
     (if_gcd#(true(), x, y) -> gcd#(minus(x, y), y), gcd#(s x, s y) -> le#(y, x))
     (if_gcd#(true(), x, y) -> gcd#(minus(x, y), y), gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y))
     (if_gcd#(false(), x, y) -> gcd#(minus(y, x), x), gcd#(s x, s y) -> le#(y, x))
     (if_gcd#(false(), x, y) -> gcd#(minus(y, x), x), gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y))}
    STATUS:
     arrows: 0.802469
     SCCS (3):
      Scc:
       {        gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y),
         if_gcd#(true(), x, y) -> gcd#(minus(x, y), y),
        if_gcd#(false(), x, y) -> gcd#(minus(y, x), x)}
      Scc:
       {minus#(x, s y) -> minus#(x, y)}
      Scc:
       {le#(s x, s y) -> le#(x, y)}
      
      SCC (3):
       Strict:
        {        gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y),
          if_gcd#(true(), x, y) -> gcd#(minus(x, y), y),
         if_gcd#(false(), x, y) -> gcd#(minus(y, x), x)}
       Weak:
       {           le(0(), y) -> true(),
                 le(s x, 0()) -> false(),
                 le(s x, s y) -> le(x, y),
                     pred s x -> x,
                minus(x, 0()) -> x,
                minus(x, s y) -> pred minus(x, y),
                  gcd(0(), y) -> y,
                gcd(s x, 0()) -> s x,
                gcd(s x, s y) -> if_gcd(le(y, x), s x, s y),
         if_gcd(true(), x, y) -> gcd(minus(x, y), y),
        if_gcd(false(), x, y) -> gcd(minus(y, x), x)}
       Fail
      
      
      SCC (1):
       Strict:
        {minus#(x, s y) -> minus#(x, y)}
       Weak:
       {           le(0(), y) -> true(),
                 le(s x, 0()) -> false(),
                 le(s x, s y) -> le(x, y),
                     pred s x -> x,
                minus(x, 0()) -> x,
                minus(x, s y) -> pred minus(x, y),
                  gcd(0(), y) -> y,
                gcd(s x, 0()) -> s x,
                gcd(s x, s y) -> if_gcd(le(y, x), s x, s y),
         if_gcd(true(), x, y) -> gcd(minus(x, y), y),
        if_gcd(false(), x, y) -> gcd(minus(y, x), x)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [if_gcd](x0, x1, x2) = x0 + 1,
         
         [le](x0, x1) = x0 + 1,
         
         [minus](x0, x1) = x0 + 1,
         
         [gcd](x0, x1) = 0,
         
         [s](x0) = x0 + 1,
         
         [pred](x0) = x0 + 1,
         
         [true] = 0,
         
         [0] = 1,
         
         [false] = 0,
         
         [minus#](x0, x1) = x0 + 1
        Strict:
         minus#(x, s y) -> minus#(x, y)
         2 + 1y + 0x >= 1 + 1y + 0x
        Weak:
         if_gcd(false(), x, y) -> gcd(minus(y, x), x)
         1 + 0y + 1x >= 0 + 0y + 0x
         if_gcd(true(), x, y) -> gcd(minus(x, y), y)
         1 + 0y + 1x >= 0 + 0y + 0x
         gcd(s x, s y) -> if_gcd(le(y, x), s x, s y)
         0 + 0y + 0x >= 2 + 0y + 1x
         gcd(s x, 0()) -> s x
         0 + 0x >= 1 + 1x
         gcd(0(), y) -> y
         0 + 0y >= 1y
         minus(x, s y) -> pred minus(x, y)
         2 + 1y + 0x >= 2 + 1y + 0x
         minus(x, 0()) -> x
         2 + 0x >= 1x
         pred s x -> x
         2 + 1x >= 1x
         le(s x, s y) -> le(x, y)
         2 + 0y + 1x >= 1 + 0y + 1x
         le(s x, 0()) -> false()
         2 + 1x >= 0
         le(0(), y) -> true()
         2 + 0y >= 0
       Qed
     
     
     SCC (1):
      Strict:
       {le#(s x, s y) -> le#(x, y)}
      Weak:
      {           le(0(), y) -> true(),
                le(s x, 0()) -> false(),
                le(s x, s y) -> le(x, y),
                    pred s x -> x,
               minus(x, 0()) -> x,
               minus(x, s y) -> pred minus(x, y),
                 gcd(0(), y) -> y,
               gcd(s x, 0()) -> s x,
               gcd(s x, s y) -> if_gcd(le(y, x), s x, s y),
        if_gcd(true(), x, y) -> gcd(minus(x, y), y),
       if_gcd(false(), x, y) -> gcd(minus(y, x), x)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [if_gcd](x0, x1, x2) = x0 + x1 + 1,
        
        [le](x0, x1) = x0 + x1 + 1,
        
        [minus](x0, x1) = x0 + 1,
        
        [gcd](x0, x1) = 0,
        
        [s](x0) = x0 + 1,
        
        [pred](x0) = x0 + 1,
        
        [true] = 1,
        
        [0] = 1,
        
        [false] = 1,
        
        [le#](x0, x1) = x0 + 1
       Strict:
        le#(s x, s y) -> le#(x, y)
        2 + 0y + 1x >= 1 + 0y + 1x
       Weak:
        if_gcd(false(), x, y) -> gcd(minus(y, x), x)
        2 + 0y + 1x >= 0 + 0y + 0x
        if_gcd(true(), x, y) -> gcd(minus(x, y), y)
        2 + 0y + 1x >= 0 + 0y + 0x
        gcd(s x, s y) -> if_gcd(le(y, x), s x, s y)
        0 + 0y + 0x >= 3 + 1y + 2x
        gcd(s x, 0()) -> s x
        0 + 0x >= 1 + 1x
        gcd(0(), y) -> y
        0 + 0y >= 1y
        minus(x, s y) -> pred minus(x, y)
        2 + 1y + 0x >= 2 + 1y + 0x
        minus(x, 0()) -> x
        2 + 0x >= 1x
        pred s x -> x
        2 + 1x >= 1x
        le(s x, s y) -> le(x, y)
        3 + 1y + 1x >= 1 + 1y + 1x
        le(s x, 0()) -> false()
        3 + 1x >= 1
        le(0(), y) -> true()
        2 + 1y >= 1
      Qed